https://file.aiquickdraw.com/mathbot/file/1729426643956qa4dk5ab.jpg

Let's break down the two problems and solve them step-by-step.

### Part a)
The expression is:  
\[
(4 \times 10^4) \times (6 \times 10^2)
\]

- Multiply the coefficients: \( 4 \times 6 = 24 \)
- Add the exponents of 10: \( 4 + 2 = 6 \)

So, the result is:
\[
24 \times 10^6
\]

This corresponds to option **C**.

### Part b)
The expression is:  
\[
(3 \times 10^7) \div (6 \times 10^3)
\]

- Divide the coefficients: \( \frac{3}{6} = 0.5 \)
- Subtract the exponents of 10: \( 7 - 3 = 4 \)

So, the result is:
\[
0.5 \times 10^4
\]

This corresponds to option **B**.

### Final Answers:
- a) **C**  
- b) **B**

Would you like further details or have any additional questions? Here are some related questions to expand your understanding:

1. How do you handle multiplication of numbers in scientific notation?
2. What happens when you divide numbers in scientific notation?
3. How do you convert between scientific notation and standard form?
4. Why do the rules of exponents apply when multiplying or dividing scientific notation?
5. How do you handle negative exponents in scientific notation?

**Tip:** When multiplying or dividing in scientific notation, always remember to treat the coefficients and exponents separately—multiply/divide the coefficients and add/subtract the exponents!

For each calculation, choose the correct answer written in standard form. a) (4 × 10^4) × (6 × 10^2) b) (3 × 10^7) ÷ (6 × 10^3)

Learn how to solve scientific notation problems like (4 × 10^4) × (6 × 10^2) and (3 × 10^7) ÷ (6 × 10^3) using the laws of exponents. This explanation breaks down multiplication and division in scientific notation with clear examples.

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